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Follow @chewxy on Twitter Yepoko Lessons For Machine Learning on Small Data Xuanyi Chew YOW! Data 2021

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Follow @chewxy on Twitter The Puzzle Term Number rureponga talu 10 malapunga yepoko 15 supu 20 tokapunga telu 21 alapunga yepoko 27 polangipula talu 30 tokapu rureponga yepoko 35 tokapu malapu 40 tokapu talu 48 tokapu alapunga talu 50 tokapu talu tokapunga telu 69 tokapu talu polangipunga yepoko 79 tokapu yepoko alapunga telu 97

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Follow @chewxy on Twitter The Puzzle Term Number rureponga talu 10 malapunga yepoko 15 supu 20 tokapunga telu 21 alapunga yepoko 27 polangipula talu 30 tokapu rureponga yepoko 35 tokapu malapu 40 tokapu talu 48 tokapu alapunga talu 50 tokapu talu tokapunga telu 69 tokapu talu polangipunga yepoko 79 tokapu yepoko alapunga telu 97 Translate: ● tokapu polangipu ● tokapu talu rureponga telu ● tokapu yepoko malapunga talu ● tokapu yepoko polangipunga telu ● 13 ● 66 ● 72 ● 76 ● 95

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Follow @chewxy on Twitter The Puzzle - One More Thing Term Number rureponga talu 10 malapunga yepoko 15 supu 20 tokapunga telu 21 alapunga yepoko 27 polangipula talu 30 tokapu rureponga yepoko 35 tokapu malapu 40 tokapu talu 48 tokapu alapunga talu 50 tokapu talu tokapunga telu 69 tokapu talu polangipunga yepoko 79 tokapu yepoko alapunga telu 97 Translate: ● tokapu polangipu ● tokapu talu rureponga telu ● tokapu yepoko malapunga talu ● tokapu yepoko polangipunga telu ● 13 ● 66 ● 72 ● 76 ● 95 telu < yepoko

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Follow @chewxy on Twitter Neural Language Models to the Rescue

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Follow @chewxy on Twitter The ML Tasks 1. Categorization 2. Regression 3. Translation (sequence to sequence)

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Follow @chewxy on Twitter Neural Language Models: The Process 1. Download a pre-trained model 2. Fine-tune it to the task using examples (all 13 of them!) 3. ??? 4. Profit!!!

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Follow @chewxy on Twitter BERT Results Test Predicted Result tokapu polangipu 55.21 ✗ tokapu talu rureponga telu 54.44 ✗ tokapu yepoko malapunga talu 57.98 ✗ tokapu yepoko polangipunga telu 58.22 ✗

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Follow @chewxy on Twitter GPT-3 > “If two times three is six, what is four times four” “Sixteen”

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Follow @chewxy on Twitter GPT-3 > if 'rureponga talu' means 10 and 'malapunga yepoko' means 15 and 'supu' means 20 and 'tokapunga telu' means 21 and 'alapunga yepoko' means 27 and 'polangipula talu' means 30 and 'tokapu rureponga yepoko' means 35 and 'tokapu malapu' means 40 and 'tokapu talu' means 48 and 'tokapu alapunga talu' means 50 and 'tokapu talu tokapunga telu' means 69 and 'tokapu talu polangipunga yepoko' means 79 and 'tokapu yepoko alapunga telu' means 97, then what does 'tokapu polangipu' mean? "I understand! It means 'twice 10'!" > “what does ‘tokapu talu rureponga telu’ mean?” "Ah! I know the answer to this! It's 'uproot 100 10 rods long trees'."

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Follow @chewxy on Twitter GPT-3 > if 'rureponga talu' means 10 and 'malapunga yepoko' means 15 and 'supu' means 20 and 'tokapunga telu' means 21 and 'alapunga yepoko' means 27 and 'polangipula talu' means 30 and 'tokapu rureponga yepoko' means 35 and 'tokapu malapu' means 40 and 'tokapu talu' means 48 and 'tokapu alapunga talu' means 50 and 'tokapu talu tokapunga telu' means 69 and 'tokapu talu polangipunga yepoko' means 79 and 'tokapu yepoko alapunga telu' means 97, then what does 'tokapu talu rureponga telu' mean? "I know the answer! Here's a guess: 100 rods long, 10 inches in diameter, made of wood, with three holes." > "what does 'tokapu polangipu' mean?" "I think it means 'two times 100'."

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Follow @chewxy on Twitter GPT-3 > if 'rureponga talu' means 10 and 'malapunga yepoko' means 15 and 'supu' means 20 and 'tokapunga telu' means 21 and 'alapunga yepoko' means 27 and 'polangipula talu' means 30 and 'tokapu rureponga yepoko' means 35 and 'tokapu malapu' means 40 and 'tokapu talu' means 48 and 'tokapu alapunga talu' means 50 and 'tokapu talu tokapunga telu' means 69 and 'tokapu talu polangipunga yepoko' means 79 and 'tokapu yepoko alapunga telu' means 97, then what does 'tokapu polangipu' mean? Let me take a look at my old records. Yes, 'tokapu polangipu' means 100. > what does ‘tokapu talu rureponga telu’ mean? Sorry, I can’t find the answer for this.

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Follow @chewxy on Twitter GPT-3 ... Socrates: tokapu alapunga talu Aristotle: 50 Socrates: tokapu talu tokapunga telu Aristotle: 69 Socrates: tokapu talu polangipunga yepoko Aristotle: 79 Socrates: tokapu yepoko alapunga telu Aristotle: 97 Socrates: tokapu polangipu Aristotle: I think it means 'Socrates is a dung beetle, Aristotle is a snake, and I am a dodo.'

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Follow @chewxy on Twitter Random Forests 1. Byte-pair encode text to be used as features 2. Encode position of pairs in sentence 3. ??? 4. Profit!

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Follow @chewxy on Twitter Random Forests Feature Matrix . C:Syl1 N:Pos1 C:Syl2 N:Pos2 C:Syl3 N:Pos3 ... C:Syl12 N:Pos12 N:Answer 1 146 0 145 0 129 0 ... 0 0 10 2 144 0 136 0 121 1 ... 0 0 15 3 115 0 117 0 140 0 ... 0 0 20 4 148 0 135 0 136 0 ... 0 0 21 5 142 0 136 0 121 1 ... 0 0 27 6 150 0 149 0 137 0 ... 0 0 30 7 148 0 135 0 146 1 ... 0 0 35 8 148 0 135 0 144 1 ... 0 0 40 9 148 0 135 0 116 1 ... 0 0 48 10 148 0 135 0 142 1 ... 0 0 50 11 148 0 135 0 116 1 ... 0 0 69 12 148 0 135 0 116 1 ... 111 3 79 13 148 0 135 0 121 1 ... 0 0 97

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Follow @chewxy on Twitter Random Forests - Results Test Predicted Result tokapu polangipu 36.74 ✗ tokapu talu rureponga telu 61.08 ✗ tokapu yepoko malapunga talu 57.62 ✗ tokapu yepoko polangipunga telu 52.09 ✗

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Follow @chewxy on Twitter Human (me) ● Finished translation in about an 40 mins. ● Used basic statistics. ● Required basic linguistics knowledge. ● Required backtracking. ● Required pattern matching. ● Required basic arithmetics. ● Required basic algebra.

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Follow @chewxy on Twitter How I Solved It

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Follow @chewxy on Twitter Offshoot On Orthography Term Number rureponga talu 10 malapunga yepoko 15 supu 20 tokapunga telu 21 alapunga yepoko 27 polangipula talu 30 tokapu rureponga yepoko 35 tokapu malapu 40 tokapu talu 48 tokapu alapunga talu 50 tokapu talu tokapunga telu 69 tokapu talu polangipunga yepoko 79 tokapu yepoko alapunga telu 97 Term Number ɾʊɾeβɔŋathɑkʟ̝ ̊ʊ 10 ɱɑkʟ̝ ̊aβʊŋaʎepɔkɔ 15 thʊβʊ 20 thɔɡaβʊŋathekʟ̝ ̊ʊ 21 ɑkʟ̝ ̊ɑβʊŋaʎepɔkɔ 27 phɔkʟ̝ ̊ɑŋɪβʊkʟ̝ ̊athɑkʟ̝ ̊ʊ 30 thɔɡaβʊɾʊɾeβɔŋaʎepɔkɔ 35 thɔɡaβʊɱɑkʟ̝ ̊aβʊ 40 thɔɡaβʊthɑkʟ̝ ̊ʊ 48 thɔɡaβʊɑkʟ̝ ̊ɑβʊŋathɑkʟ̝ ̊ʊ 50 thɔɡaβʊthɑkʟ̝ ̊ʊthɔɡaβʊɱɑthekʟ̝ ̊ʊ 69 thɔɡaβʊthɑkʟ̝ ̊ʊphɔkʟ̝ ̊ɑŋɪβʊŋaʎepɔkɔ 79 thɔɡaβʊʎepɔkɔɑkʟ̝ ̊ɑβʊŋathekʟ̝ ̊ʊ 97

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Follow @chewxy on Twitter Syllables alapunga

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Follow @chewxy on Twitter Syllables alapunga [ɑ, kʟ ̝ ̊ɑ, βʊ, ŋa]

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Follow @chewxy on Twitter Byte Pair Encoding alapunga

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Follow @chewxy on Twitter Byte Pair Encoding alapunga [al, la, ap, pu, un, ng, ga]

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Follow @chewxy on Twitter Byte Pair Encoding alapunga [al, la, ap, pu, un, ng, ga] [󰎃, 💎, 👐]

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Follow @chewxy on Twitter Byte Pair Encoding alapunga [al, la, ap, pu, un, ng, ga] [󰎃, 💎, 👐] 󰎃 al 💎 🇿u 👐 🆖a 🇿 ap 🆖 ng

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Follow @chewxy on Twitter Byte Pair Statistics pu 17 ap 14 ok 14 al 11 ng 11 ga 9 ka 9 lu 9 po 9 to 9 la 8 ep 7 un 7 ta 6 ko 5 ye 5 el 3 te 3 ur 2 an 2 gi 2 ip 2 ma 2 ol 2 on 2 re 2 ru 2 su 1 ul 1 up 1

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Follow @chewxy on Twitter Syllable Statistics pu 17 ap 14 ok 14 al 11 ng 11 ga 9 ka 9 lu 9 po 9 to 9 la 8 ep 7 un 7 ta 6 ko 5 ye 5 el 3 te 3 ur 2 an 2 gi 2 ip 2 ma 2 ol 2 on 2 re 2 ru 2 su 1 ul 1 up 1 nga 9 ngi 2 a 2

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Follow @chewxy on Twitter Syllable Statistics pu 17 ap 14 ok 14 al 11 ng 11 ga 9 ka 9 lu 9 po 9 to 9 la 8 ep 7 un 7 ta 6 ko 5 ye 5 el 3 te 3 ur 2 an 2 gi 2 ip 2 ma 2 ol 2 on 2 re 2 ru 2 su 1 ul 1 up 1 nga 9 ngi 2 a 2

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Follow @chewxy on Twitter Recursive Pattern Matching Some “phrases” are repeated. Term Number rureponga talu 10 malapunga yepoko 15 supu 20 tokapunga telu 21 alapunga yepoko 27 polangipula talu 30 tokapu rureponga yepoko 35 tokapu malapu 40 tokapu talu 48 tokapu alapunga talu 50 tokapu talu tokapunga telu 69 tokapu talu polangipunga yepoko 79 tokapu yepoko alapunga telu 97

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Follow @chewxy on Twitter Recursive Pattern Matching Some “phrases” are repeated. We now have “word” units. Term Number rureponga talu 10 malapunga yepoko 15 supu 20 tokapunga telu 21 alapunga yepoko 27 polangipula talu 30 tokapu rureponga yepoko 35 tokapu malapu 40 tokapu talu 48 tokapu alapunga talu 50 tokapu talu tokapunga telu 69 tokapu talu polangipunga yepoko 79 tokapu yepoko alapunga telu 97

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Follow @chewxy on Twitter Recursive Pattern Matching Some “phrases” are repeated. We now have “word” units. We now have “sub-word” units. Term Number rureponga talu 10 malapunga yepoko 15 supu 20 tokapunga telu 21 alapunga yepoko 27 polangipula talu 30 tokapu rureponga yepoko 35 tokapu malapu 40 tokapu talu 48 tokapu alapunga talu 50 tokapu talu tokapunga telu 69 tokapu talu polangipunga yepoko 79 tokapu yepoko alapunga telu 97

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Follow @chewxy on Twitter Solving It - Apply Broad Pattern Matching tokapu talu tokapunga telu 48 21 69 + Bigrams should be considered. tokapunga telu 21 tokapu talu 48 tokapu talu tokapunga telu 69 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It - First Level Pattern Matching tokapu talu tokapunga telu 48 + 21 69 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. ? How tightly do bigrams bind? tokapunga telu 21 tokapu talu 48 tokapu talu tokapunga telu 69 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It - Apply New Information on New Problem tokapu talu polangipunga yepoko 48 + x 79 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. ? How tightly do bigrams bind? tokapunga telu 21 tokapu talu 48 tokapu talu tokapunga telu 69 tokapu talu polangipunga yepoko 79 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It - Apply New Information on New Problem tokapu talu polangipunga yepoko 48 + 31 79 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. ? How tightly do bigrams bind? tokapunga telu 21 tokapu talu 48 tokapu talu tokapunga telu 69 tokapu talu polangipunga yepoko 79 polangipunga yepoko 31 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It - A Leap of Faith + Bigrams should be considered. + Juxtaposition of bigrams implies addition. ? How tightly do bigrams bind? * polangipula is a typo of polangipunga polangipunga yepoko 31 polangipula talu 30 polangipunga yepoko 31 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It - A Second Leap of Faith polangipunga yepoko = 31 polangipunga talu = 30 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. ? How tightly do bigrams bind? * polangipula is a typo of polangipunga + talu < yepoko; yepoko = (succ talu) polangipunga yepoko 31 polangipula talu 30 polangipunga yepoko 31 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It - Applying New Information tokapu alapunga talu x + y 50 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. * Bigrams bind tightest to the right. * polangipula is a typo of polangipunga + talu < yepoko; yepoko = (succ talu) tokapu alapunga talu 50 alapunga yepoko 27 polangipunga yepoko 31 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It alapunga talu = x alapunga yepoko = 27 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. * Bigrams bind tightest to the right. * polangipula is a typo of polangipunga + talu < yepoko; yepoko = (succ talu) tokapu alapunga talu 50 alapunga yepoko 27 polangipunga yepoko 31 alapunga talu 26 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It tokapu alapunga talu x + 26 50 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. * Bigrams bind tightest to the right. * polangipula is a typo of polangipunga + talu < yepoko; yepoko = (succ talu) tokapu alapunga talu 50 alapunga yepoko 27 polangipunga yepoko 31 alapunga talu 26 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It- Breakthrough 1 tokapu alapunga talu 24 + 26 50 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. * Bigrams bind tightest to the right. * polangipula is a typo of polangipunga + talu < yepoko; yepoko = (succ talu) tokapu alapunga talu 50 alapunga yepoko 27 polangipunga yepoko 31 alapunga talu 26 tokapu 24 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It- Breakthrough 2 tokapu talu 24 × 2 48 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. * Bigrams bind tightest to the right. * polangipula is a typo of polangipunga + talu < yepoko; yepoko = (succ talu) + Juxtaposition of words in a bigram implies multiplication. tokapu talu 48 polangipunga yepoko 31 alapunga talu 26 tokapu 24 telu 1 talu 2 yepoko 3 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Breakthrough Number system is somewhat “positional”. Large numbers appear to be Base-24. Term Number rureponga talu 10 malapunga yepoko 15 supu 20 tokapunga telu 21 alapunga yepoko 27 polangipula talu 30 tokapu rureponga yepoko 35 tokapu malapu 40 tokapu talu 48 tokapu alapunga talu 50 tokapu talu tokapunga telu 69 tokapu talu polangipunga yepoko 79 tokapu yepoko alapunga telu 97

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Follow @chewxy on Twitter Positional Numbers 四百二十

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Follow @chewxy on Twitter Positional Numbers 四百二十 400 20

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Follow @chewxy on Twitter Positional Numbers 四百二十 4 100 2 10 + × × = 420

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Follow @chewxy on Twitter Positional Numbers 四百二十 4 100 2 10 + × × = 420

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Follow @chewxy on Twitter Positional Numbers 四百二十 4 100 2 10 + × × = 420

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Follow @chewxy on Twitter Positional Numbers 四百二十 4 100 2 10 + × × = 420

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Follow @chewxy on Twitter Positional Numbers 四百二十 4 100 2 10 + × × = 420

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Follow @chewxy on Twitter Solving It - The -nga Suffix tokapu talu tokapunga telu 21 48 + = 69

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Follow @chewxy on Twitter Solving It - The -nga Suffix tokapu talu tokapunga telu 24 2 21 × + = 69

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Follow @chewxy on Twitter Solving It - The -nga Suffix tokapu talu tokapunga telu 24 2 24 ? 1 × + + × = 69

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Follow @chewxy on Twitter Solving It- The -nga Suffix rureponga talu = 10 12 ? 2 = 10 malapunga yepoko = 15 16 ? 3 = 15 tokapunga telu = 21 24 ? 1 = 21 alapunga yepoko = 27 x ? 3 = 27 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. * Bigrams bind tightest to the right. * polangipula is a typo of polangipunga + talu < yepoko; yepoko = (succ talu) + Juxtaposition of words in a bigram implies multiplication. rureponga talu 10 malapunga yepoko 15 tokapunga telu 21 alapunga yepoko 27 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It- The -nga Suffix rureponga talu = 10 12 -4 2 = 10 malapunga yepoko = 15 16 -4 3 = 15 tokapunga telu = 21 24 -4 1 = 21 alapunga yepoko = 27 28 -4 3 = 27 + Bigrams should be considered. + Juxtaposition of bigrams implies addition. * Bigrams bind tightest to the right. * polangipula is a typo of polangipunga + talu < yepoko; yepoko = (succ talu) + Juxtaposition of words in a bigram implies multiplication, except following -nga , then it’s addition. + -nga means (-4). rureponga talu 10 malapunga yepoko 15 tokapunga telu 21 alapunga yepoko 27 * - assumption ? - open question + - newly synthesized fact

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Follow @chewxy on Twitter Solving It - The -nga Suffix tokapu talu tokapunga telu 24 2 24 ? 1 × + + × = 69

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Follow @chewxy on Twitter Solving It - The -nga Suffix tokapu talu tokapunga telu 24 2 24 -4 1 × + + + = 69

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Follow @chewxy on Twitter Inconsistencies in Positional Numbers sixty nine thousand four hundred and twenty 六万九千四百二十 (6 × 10 + 9) × 1000 + 4 × 100 + 2 × 10 6 × 10000 + 9 × 1000 + 4 × 100 + 2 × 10 69420

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Follow @chewxy on Twitter Solving It... Left as an exercise to the watcher.

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Follow @chewxy on Twitter ML/AI = “Do What You Just Did, At Scale”

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Follow @chewxy on Twitter What The Human Needed ● Which examples to work on ● Recursive problem solving (solving for something while solving for another) ● Parallel problem solving (solving for multiple things at once) ● Backtracking ● Error correction ● Feature engineering ● Prior knowledge ○ Arithmetics ○ Algebra ○ Linguistics ○ Statistics ● Putting all these together

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Follow @chewxy on Twitter What Machines Are Good At ● Which examples to work on ● Recursive problem solving (solving for something while solving for another) ● Parallel problem solving (solving for multiple things at once) ● Backtracking ● Feature engineering ● Error tolerance ● Prior knowledge* ● Putting all these together

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Follow @chewxy on Twitter AI Has a Long Way to Go Human reasoning is still needed. Reinforcement learning may learn “reasoning”.

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Follow @chewxy on Twitter Telu More Experiment

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Follow @chewxy on Twitter Inspecting the BERT Neurons Layer 11, Head 5 (EN), Head 6 (UU) “fourty eight” → “4 8” “tokapu talu” → “4 8” 4 8 [SEP] 4 8 [SEP] [CLS] four## ##ty [SEP] Eight

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Follow @chewxy on Twitter Talu Artificial Languages Base-10: One byte for units under 5, one byte-pair for units up to 10, multiply-add combinations for the rest up to 100 Base-12: One byte for units under 6, one byte-pair for units up to 12, multiply-add combinations for the rest up to 100. Two ways of doing multiply-add: prefix and postfix multiplication

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Follow @chewxy on Twitter The Basic Components Base-10 Base-12 a 1 ba 6 e 2 be 7 i 3 bi 8 o 4 bo 9 u 5 bu 10 a 1 ba 7 e 2 be 8 i 3 bi 9 o 4 bo 10 u 5 bu 11 ə 6 bə 12

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Follow @chewxy on Twitter Examples 1 - Postfix Multiplication Base-10 abu = 11 ebu = 12 bue = 20 abue = 21 obue = 24 ebube = 72 Base-12 abe = 13 ebe = 14 bee = 24 abea = 25 ebea = 26 beə = 72

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Follow @chewxy on Twitter Examples 2 - Prefix Multiplication Base-10 bua = 11 bue = 12 ebu = 20 ebua = 21 ebuo = 24 bebue = 72 Base-12 bea = 13 bee = 14 ebe = 24 ebea = 25 ebee = 26 əbe = 72

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Follow @chewxy on Twitter Can a BERT-based LM Translate These Artificial Languages? Multiply-Add Type Base-10 Base-12 Prefix multiplication (e.g. “twenty-four”) Yes No Postfix multiplication (e.g. “four-and-twenty”) No No

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Follow @chewxy on Twitter Can a LM w/ BERT Arch Translate These Artificial Languages? Multiply-Add Type Base-10 Base-12 Prefix multiplication (e.g. “twenty-four”) Yes* Yes* Postfix multiplication (e.g. “four-and-twenty”) Yes* Yes* * super over-fitted obviously

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Follow @chewxy on Twitter Yepoko Lessons

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Follow @chewxy on Twitter Use The Right Tool for the Right Job Machine learning algorithms are probably not the right tool for this puzzle. It’s the right tool for a much larger dataset. Prolog might help.

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Follow @chewxy on Twitter Careful Thought with Judiciously Placed Statistical Tools For now, we can’t replace careful thought with machines. Machines are awesome at statistics though.

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Follow @chewxy on Twitter Watch Your Biases! Bias can fuck you up in more ways than you expect.

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Follow @chewxy on Twitter Closing Thoughts

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Follow @chewxy on Twitter The Language ● Umbu-ungu/Imbo-ungu is a language in Southern Highlands of PNG. ● Base-4, Base-12, Base-24, Base-28, Base-32 number system. ● PNG is the most linguistically diverse country in the world.

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Follow @chewxy on Twitter Neural Machine Translation ● Requires parallel corpus. ● Only parallel corpus for Umbu-Ungu is The Bible. ● Rare language communities are underserved.

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Follow @chewxy on Twitter Join Me (Shameless Plug) https://gorgonia.org [email protected] @chewxy

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Follow @chewxy on Twitter Thank You

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Follow @chewxy on Twitter The Fate of Umbu-Ungu andrete - 100 (from hundred in English) tausen - 1000 (from thousand in English) Mostly Tok Pisin (from talk business)

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Follow @chewxy on Twitter The Deep Learning Bombe - An Enigma